Answer: a. 8.16%
b. $65,762.5
c. $39,700
Step-by-step explanation:
Initial investment for 15years= $12500
Investment for 5years= $20000
Interest = 8% compunded semi annually for the first 10 years and 6.5% compunded annually for the last five years.
a. EAR= [1+(nominal interest rate/the number of compounding periods)]^number of compounding periods-1
where,
nominal interest= 8 %,
number of compounding periods = 2 (semi annually)
EAR =( [ 1 + ( 0.08 / 2 ) ] ^ 2) - 1
= { ( 1 + 0.04 )^2 } - 1
= { 1.04 } ^ 2 - 1 = 1.0816 - 1
= 0.0816
= 8.16%
b. The amount on $12500 for 10 years compounded semi annually:
= $12500 + ( 12500×8.160%×10)
= $ 22,700
The amount on $32,500 for 5 Years compounded annually
=$32500 + (32500×6.5%×5)
= $43,062.50
Money in account today:
= $ 22,700 + $43,062.50
= $65,762.5
c. Let the amount be x
For the first 10 years at 8.160 %
Interest Amount = ( x × 8.160% × 10 )
= 0.8160x
For the next 5 years:
Interest Amount will be,
= (x × 6.5% × 5)
= 0.325x
Total money at end of 15 Years=85000
0.8160x + 0.3250x + x = 85000
2.141x = 85000
x = 85000/2.141
X = $ 39,700 Approx.